Ratio and proportion: Practice Questions

On a map drawn to a scale of \(1 : 40\,000\), the length of a straight road is \(6.5\text{ cm}\). Find the actual length of the road in kilometres.

The variables \( p \) and \( q \) satisfy an inverse proportion relationship such that \( p \) is inversely proportional to \( \sqrt{q} \). When \( q = 16 \), \( p = 3 \). Find the value of \( p \) when \( q = 64 \).

It is given that \( y \) is inversely proportional to the square of \( x \). When \( x = 2 \), \( y = 9 \). Find the value of \( y \) when \( x = 3 \).

A map has a scale of \( 1 : 500 \). A rectangular garden is represented on the map by an area of \( 4 \text{ cm}^2 \). Calculate the actual area of the garden in square metres.

On a map, the distance between two towns is \( 8.4\text{ cm} \). The map has a scale of \( 1 : 50,000 \). Calculate the actual distance between the two towns in kilometres.

The scale of a map is \( 1 : 250\,000 \). If the distance between two towns on the map is \( 4.8 \text{ cm} \), find the actual distance between the towns in kilometres.

A map is drawn to a scale of \( 1 : 250,000 \). The actual area of a lake is \( 18.75 \text{ km}^2 \). Calculate the area of the lake as represented on the map in \( \text{cm}^2 \).

The scale of a map is given as \( 1 : 50,000 \).
(a) If the distance between two parks on the map is \( 8.4 \) cm, calculate the actual distance between them in kilometers.
(b) A forest has an actual area of \( 12 \) km\(^2\). Calculate the area of the forest on the map in square centimeters.